$\int x^{-6}\,dx=$ $+C$
The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{{-6}}\,dx&=\dfrac{x^{{-6}+1}}{{-6}+1}+C \\\\ &=-\dfrac15x^{-5}+C \end{aligned}$ In conclusion, $\int x^{-6}\,dx=-\dfrac15x^{-5}+C$